Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | Aut(G) order 4872000 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2175 |
| unambiguous semidirect product | C3⋊Dic725 |
| derived, Hall | C3×C25×C29 ⋊ C4 |
| Hall | C25×C29 ⋊ Dic3 |
| Hall | C3×C29 ⋊ Dic25 |
| Hall | C3×C25 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic75 |
| Sylow | C25 ⋊ Dic87 |
| Sylow | C3 ⋊ Dic725 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2175 |
| commutator, hypocenter | C3×C25×C29 | C4 |
| Frattini | C2×C5 | D435 |
| Fitting | C2×C3×C25×C29 | C2 |
| socle | C2×C3×C5×C29 | D5 |
| LCS | G ▷ C3×C25×C29 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,29,2,5|a^2=e,c^5=f^4,b^a=b^2,c^a=c^4f,d^a=d^28,f^a=f^42178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic6525, C3×Dic2175, C3⋊Dic2175, … |
| maximal normal subgroup of | C3×Dic2175, Dic4350 |
| maximal quotient of | Dic6525, C3×Dic2175, C3⋊Dic2175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 8);